The invention relates to apparatuses for playing roulette and methods for arranging indicia on roulette game surfaces and roulette wheels.
Roulette is a well-known game of chance enjoyed throughout the world. The equipment used for playing roulette generally comprises a roulette wheel and a game surface.
The roulette wheel generally comprises a horizontally disposed wheel mounted in a bowl-shaped housing. The wheel is adapted to rotate about a vertical axis and includes a plurality of pockets disposed around its periphery. Each pocket has a unique number associated with the pocket, as well as a color associated therewith. Each pocket is adapted to receive a small ball which is introduced into the bowl shaped housing by an operator or croupier as the wheel is set in motion. The wheel is typically spun in one direction and the ball projected around the circumference of the housing in an opposite direction. As the ball loses speed, it rolls down the concave housing wall, eventually coming to rest in one of the pockets. The outcome or result of the spin is the number and color associated with the pocket in which the ball comes to rest.
The game surface includes a plurality of wagering areas indicating various numbers, colors, parities (the odd or even quality of a number) and groupings of numbers. One or more players make wagers on a predicted outcome of a spin of the roulette wheel. A player indicates his or her wager by placing one or more wagering devices, such as chips or markers representing an amount of the wager, at a predetermined location on the game surface corresponding to a predicted outcome of a spin of the roulette wheel.
A prior art “Standard” roulette game surface or board 10 is shown in FIG. 1. As shown the game surface includes wagering areas corresponding to the individual numbers 1 through 36. The numbers are arranged sequentially in three columns of twelve numbers each and twelve rows or streets of three numbers each. Eighteen of the numbers (1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34 and 36) correspond to a first color, typically red, and the remaining eighteen numbers (2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33 and 35 correspond to a second color, typically black. In the prior art arrangement, there are eight even red numbers (12, 14, 16, 18, 30, 32, 34 and 36), ten odd red numbers (1, 3, 5, 7, 9, 19, 21, 23, 25, and 27), ten even black numbers (2, 4, 6, 8, 10, 20, 22, 24, 26 and 28) and eight odd black numbers (11, 13, 15, 17, 29, 31, 33 and 35).
A player may place a wager on a particular number by placing one or more chips or markers within the wagering area corresponding to that number. The table layout permits the player to place bets on individual numbers or combinations or groupings of individual numbers. For example, a player can wager on a column of numbers by placing one or more chips or markers adjacent to the column of numbers, on a row of numbers by placing one or more chips or markers adjacent to the row of numbers, on two rows of numbers by placing one or more chips or markers adjacent to the two rows of numbers, and on four adjoining numbers by placing one or more chips or markers at the intersection of the four adjoining numbers.
As shown in FIG. 1, wagering areas are also typically provided for betting on the number 0 (and/or the number 00 in an American style wheel as described more fully herein), on a particular color outcome (for example red or black), on an even or odd number outcome, on an outcome comprising a number from 1 to 18, on an outcome comprising a number from 19 to 36 and on a particular set or block of numbers (for example first twelve number 1 through 12, second twelve numbers 13 through 24 or last twelve numbers 25 through 36).
Winning wagers in the game of roulette are paid out at predetermined multiples based on the probability of the particular predicted outcome. For example, a winning wager for an individual number may pay out at a ratio of 35 to 1; a winning wager for a row of three numbers may pay out at a ratio of 11 to 1; a winning wager for a group of four adjacent numbers may pay out at a ratio of 8 to 1; a winning wager for two adjacent rows of number may pay out at a ratio of 5 to 1; a winning wager for the combination of numbers 1 to 18 or the combination of numbers from 19 to 36 may pay out at a ratio of 1 to 1; a winning wager on a column of numbers may pay out at a ratio of 2 to 1; a winning wager on a block of twelve consecutive numbers (first twelve, second twelve or last twelve) may pay out at a ratio of 2 to 1, and a winning wager on an odd number; an even number, a red number or a black number may pay out even money. Other wager combinations and associated payout ratios may also be used. Table I below shows an example betting arrangements and corresponding payouts ratios:
TABLE IIndividual number bet35:1  2-number bet17:1  3-number bet11:1  4-number bet8:1 6-number bet5:112-number bet2:118-number bet1:1
The prior art (standard) American roulette wheel arrangement is shown in FIG. 1A. As shown, the prior art American wheel includes both zero (0) and double zero (00) house numbers arranged opposite each other and thirty six numbers from 1 to 36 arranged around the perimeter of the wheel for a total of thirty eight pockets.
The numbers from 1 to 36 are arranged at standardized positions on the prior art American wheel as shown in FIG. 1A. In the standard American wheel the compartments are numbered and colored clockwise from 0 as follows: 0, 28, 9, 26, 30, 11, 7, 20, 32, 17, 5, 22, 34, 15, 3, 24, 36, 13, 1, 00, 27, 10, 25, 29, 12, 8, 19, 31, 18, 6, 21, 33, 16, 4, 23, 35, 14, 2. The house numbers (0, 00) are typically green in color. The numbers 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34 and 36 are red, and the numbers 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33 and 35 are black. Black and red numbers alternate, and directly across the wheel from each odd number is the next highest even number (for example the number 10 is directly across the wheel from the number 9).
FIG. 1B shows the prior art European roulette wheel arrangement. In the standard European roulette wheel as shown in FIG. 1B, the wheel compartments are numbered and colored clockwise from 0 as follows: 0, 32, 15, 19, 4, 21, 2, 25, 17, 34, 6, 27, 13, 36, 11, 30, 8, 23, 10, 5, 24, 16, 33, 1, 20, 14, 31, 9, 22, 18, 29, 7, 28, 12, 35, 3, 26. As shown, the European roulette wheel arrangement includes only one house number, the single zero (0) and thirty six numbers, for a total of thirty seven pockets. This results in a significantly lower house advantage for the European wheel (house edge= 1/37 or approximately 2.70%) as compared to the American wheel (house edge= 2/38 approximately 5.26%). The individual numbers from 1 to 36 in the prior art European roulette wheel have the same colors as they have in the prior art American roulette wheel, and the numbers are also arranged at standardized positions; however the arrangement of numbers around the wheel differs substantially in the European roulette wheel as compared to the American wheel.
As described in detail in applicant's issued U.S. Pat. No. 7,588,250, the contents of which are incorporated by reference as if fully set forth herein, the arrangement of numbers and colors on the prior art roulette game surface shown in FIG. 1 (and used with both the prior art American roulette wheel arrangement shown in FIG. 1A and the prior art European roulette wheel arrangement shown in FIG. 1B) is not optimized or balanced with respect to the entire game surface, the individual columns and the individual dozen wagering groups (1-12, 13-24 and 25-36), as set forth below. In particular, the distribution of red, black, odd and even numbers on the prior art roulette game surface is unbalanced and as a result experienced players may combine bets on red, black, even and odd numbers, columns and dozen groups to increase the player's chances of winning a bet. In addition, an inexperienced player may lack the knowledge to take advantage of these relationships, resulting in a greater advantage for the casino or house.
In one example, as shown in FIG. 1, the prior art roulette game surface arrangement has ten red odd numbers (1, 3, 5, 7, 9, 19, 21, 23, 25 and 27), but only eight red even numbers (12, 14, 16, 18, 30, 32, 34 and 36). Additionally, the prior art arrangement has ten black even numbers (2, 4, 6, 8, 10, 20, 22, 24, 26, 28), but only eight black odd numbers (11, 13, 15, 17, 29, 31, 33 and 35). This imbalance in the distribution of red, black, odd and even numbers throws off the balance of the individual columns and dozen wagering areas.
Further, the relationships among adjacent numbers on the prior art roulette wheels and their corresponding positions, groupings and characteristics on the prior art roulette game surface may allow experienced players to combine bets on red, black, even and odd numbers, columns and dozen groups to increase the player's chances of winning. For example in the prior art arrangements, players may “flower” the wheel by placing bets corresponding to a group of numbers positioned on the roulette wheel adjacent or in close proximity to one another. By utilizing progressive betting techniques and taking advantage of the relationship between the positions of the numbers on the roulette wheel and the various betting schemes (red, black, odd, even, column, dozen group) a professional or experienced player may increase his or her odds of winning.
There exists a need for improved roulette board game surface and wheel arrangements having a more “balanced” layout wherein red and black and even and odd numbers are evenly distributed. Moreover, the need exists for an improved roulette game surface and wheel arrangement wherein relationships between adjacent pairs or groups of numbers on the wheel and the arrangement and characteristics of numbers on the game surface are eliminated.
More particularly, one aspect of the Roulette Wheel game that has yet to be addressed in the gaming industry with respect to the layout of the game surface board and Roulette wheel indicia in the standard roulette (36 non-house numbers) embodiments is the effect of bias. For example, as a standard mechanical roulette wheel of 36 non-house numbers is designed so that the 37 or 38 possible numerical outcomes occur randomly and unpredictably (i.e., each outcome is equally likely to occur and information about previous outcomes does not change the estimated probability of the next outcome), a tendency for a particular number to occur more or less likely than 1/37 of the time in a standard European wheel, or 1/38 of the time in a standard American wheel, is referred to as a “bias”. Other types of non-randomness involving patterns of correlation between multiple outcomes, even while individual numbers remain equally likely on average, are also possible. Thus, sources of bias and non-randomness could cause roulette outcomes to become more predictable.
For mechanical roulette wheels, there is no software or numerical calculation occurring. The randomness is determined by the independence of the physical processes involved: the speed of rotation of the wheel; the deceleration of the rotation over time; the time at which a croupier releases the ball; the speed and spin with which the croupier releases the ball; the deceleration of the ball as it rotates before dropping; the bounces the ball makes when it hits the wheel; and the deflections of the ball by any baffles or other built-in irregularities in the bowl the wheel spins within.
Because the state of the system depends only on continuous physical variables such as rotation speed and ball position, there is no way for a mechanical roulette wheel to encode information about multiple previous outcomes. Therefore, the kinds of long range correlations between multiple outcomes that can occur in algorithmic random number generators are not significant in mechanical roulette wheels. Once the ball has fallen into a numbered slot, any information related to what slots it had previously fallen into is effectively erased. Although there may be a non-random relationship between one outcome and the next outcome, correlations and relationships between spins that are not consecutive are not to be expected, and tests for randomness in mechanical roulette wheels focus only on individual outcomes and correlations between consecutive outcomes. A deviation of the outcome probabilities from equality is referred to as an “absolute bias”, and a non-random relationship between consecutive outcomes referred to as a “relative bias”.
Absolute bias results from asymmetries in the roulette wheel. These can occur due to local irregularities (dents, nicks, slight differences in the size or shape of the numbered compartments, variations in the density or hardness of the material used to make the walls between compartments) or overall deviations (warping or deviations from circularity; unbalanced mounting so the wheel is not completely level).
The different sources of absolute bias will tend to result in different patterns of non-randomness in the outcome probabilities. These sources of absolute bias include:
1) A wheel which is not mounted levelly will show a circular or “dipole” variation in the probabilities, with one half of the wheel being more likely than the other half, and the highest-probability and lowest probability numbers being concentrated in opposite regions of the wheel.2) A wheel which is warped, and so slightly elliptical rather than circular in shape, will show a quadruple variation in the probabilities, with the higher probability numbers concentrated in opposite regions of the wheel corresponding to one axis of the ellipse, and the lower probability numbers concentrated in the complementary regions corresponding to the other axis of the ellipse.3) A wheel which was manufactured to loose tolerances or assembled with insufficient precision will tend to have many numbers with small deviations from the uniform probabilities.4) A wheel which has been in operation for a long time and suffers from wear and tear will tend to have a few numbers with significant deviations from the uniform probabilities.5) A wheel which has suffered some accident or external blow or tampering will tend to have a single number with a large deviation from the uniform probabilities.
Even when a roulette wheel is perfectly symmetrical and physically balanced, so that over time all numbers occur with equal probability, relative biases related to correlations between consecutive spins may occur. These are caused by insufficient variability in three continuous quantities determining roulette outcomes: rotational velocity of the wheel, speed with which the ball is released, and timing of the ball release relative to when the ball was removed from the slot it fell into on the previous spin. Too much uniformity in these variables will result in the quantity “total number of revolutions the ball makes” having a sufficiently non-uniform distribution that the relative angle between the outcome from the previous spin and the outcome from the current spin is also nonuniform in a detectable way.
Thus, the biases typically found in roulette wheels: 1) Bias due to irregularities in individual compartments or locations on the wheel; and 2) Bias due to an overall imbalance or asymmetry in the wheel's rotation (which may come from either imperfect manufacture or inaccurate installation) or, because of wear and tear on the wheel over time (e.g., people bumping into the wheel, vibrations, etc) causes drifting away from equal probabilities. The first kind of bias affects individual number bets. The second bias affects multiple number bets with “regions” of the wheel rather than individual numbers deviating from the expected probability. However, the second bias has a greater impact on the multiple number bets.
It would be highly desirable to provide a Roulette wheel apparatus, and a method for arranging indicia on a Roulette wheel that is more balanced than the prior art (standard) Roulette wheels such that the impact of the bias in the physical wheel is minimized.
It would be further highly desirable to provide a Roulette wheel apparatus, and a method for arranging indicia on a Roulette wheel that is more balanced than the prior art (standard) Roulette wheels, such that the impact of the second bias in the physical wheel is minimized.
It would be further desirable to provide a Roulette wheel apparatus, and a method for arranging indicia on a 36 number balanced Roulette wheel that is more balanced than the prior art (standard) Roulette wheels, such that the impact of the bias in the physical wheel is minimized by reducing impact of a biased wheel on the House Edge for various types of betting arrangements.
It would be further desirable to provide a Roulette wheel apparatus, and a method for arranging indicia on a 36 number balanced Roulette wheel to reduce the impact of a biased wheel on multi-number bets, by spreading the physical location of the numbers in a multi-number bet more evenly around the roulette wheel.
It would be further desirable to provide a Roulette wheel apparatus, and a method for arranging indicia on a 36 number balanced Roulette wheel to minimize the impact of bias on combinations of multi-number bets.